T test.

Hello, I was told by my lecturer that I need to do some T-tests on my data in order to find out if it is significant or not. The data is basically student's grades and I am trying to prove that intrinsic students achieve higher grades in comparison to extrinsic students.

So I used an online calculator to calculate the T test on this data:

Data 1 (extrinsic students):

49.5
52
55
55.5
55.5
59
59.5
60
60.5
63.5
65.75
66
67
69.5
76.5
78
78

Data 2: (Intrinsic students)

55
59.5
60
63.5
64
65
65.5
68
69
72.5
76.5
76.5
77.5
77.5
80
82
83

For this data I set it as of unequal variance and a 2 tail test. I am not too sure If i used the right tail test. The following figure was returned:

Online calculator: = 0.01967
Excel: 0.009833876

I have no idea what either of these numbers mean, can anyone help?

Thanks,
Sean

Last edited by mr fantastic; April 27th 2011 at 07:40 PM.
Reason: Title.

Based on your data (group 1 vs group 2), I believe that you are testing the alternative hypothesis that the mean for the group 1 is different from the mean of the group 2, or vice-versa - assuming that this difference can be in any direction. In other words, your null hypothesis is that the difference between those means is zero. Running your data in R, I got a two-sided P-value of 0.0196677511603729 (t=-2.4559, with 32 degrees-of-freedom). The value of 0.0098 you mention refers to the one-sided test, in which your alternative hypothesis is that the mean for the group 1 (extrinsic) is smaller (one direction only) than group 2, that is, your alternative is that the difference (mean 1)-(mean 2) < 0. I got these results assuming equal variances. Use of Welch's approximation (unequal variances) gives slightly different results: (P = 0.0193 and P = 0.0097 , t= -2.4559 and 33.9832 degrees-of-freedom)